You can, but g++ does name mangling on C++ files, but not on C files. The C++ code, including the sketch, won't be able to call the C functions, unless you use the proper directives in the header file.

If its really a library, why not put it in its own directory under libraries... That's way it can be shared.

Once its built the libraries folder is suitable, not while its in development; example files, additional library files all require a restart to be usable in the IDE, a simple sketch just needs re-opening. This may not seem like much, but can get very frustrating when actively modifying numerous files.